Mathematics
Open problems, research attempts and community review.
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-5251 Bit-Width-Independent Verification of Integer Multipliers
- Math-5252 Random CNF Lower Bounds beyond Cutting Planes
- Math-5253 PSD Rank Bounds for Polynomial-Size Selector Matrices
- Math-5254 Ordered-Median Facility Location
- Math-5255 Certificates of Polynomial Nonnegativity in Copositive Optimization
- Math-5256 Deterministic Components of Stochastic Optimization
- Math-5257 Unified Simplicity Models for Massive Inverse Problems
- Math-5258 Provable Advantages of Convolutional Arithmetic Circuits
- Math-5259 Statistical Recovery of High-Dimensional Network Structure
- Math-5260 Local Algorithms for Semidefinite Programming
- Math-5261 Polynomial-Time Estimation in Binary Latent-Variable Models
- Math-5262 The Polynomial Hirsch Conjecture
- Math-5263 Defining High-Dimensional Expanders Through Local Spectra
- Math-5264 Explicit Equations Separating Matrix Multiplication from Low-Rank Tensors
- Math-5265 Sequential Decoding of Nonbinary Convolutional Codes
- Math-5266 Convolutional Codes for Retrieval, Sensing, and Rank Metrics
- Math-5267 Restricted Models of Vertex-Distribution-Free Testing
- Math-5268 Automatic Recognition of Numerically Unstable Quadratic Programs
- Math-5269 Adaptive Refinement and Global Optimization of Topological Shapes
- Math-5270 Low-Temperature Sampling by Randomly Initialized Glauber Dynamics
- Math-5271 Multiplicity Obstructions in Geometric Complexity Theory
- Math-5272 Primal and Dual Geometry of SONC Relaxations
- Math-5273 Global Optimality of Domain-Decomposition Transport Algorithms
- Math-5274 Robustness-Driven Overparameterization in Two-Layer Neural Networks
- Math-5275 Geometric Analogues of Finite Effective Complexity
- Math-5276 Comparative Advantages of Physics-Based and Machine-Learned Models
- Math-5277 High-Dimensional Regression and PDE Learning Without Dimensional Curse
- Math-5278 Algorithms for Symmetry-Reduced Semidefinite Programs
- Math-5279 Quantum Complexity of High-Precision Matrix Scaling
- Math-5280 Unspecified Combinatorial Optimization Problem
- Math-5281 Half-Integral Extreme Points for Feedback Vertex Set
- Math-5282 Approximating Submodular Functions by Matroid Rank Functions
- Math-5283 Probabilistic Box Models
- Math-5284 Dimension–Complexity Tradeoffs in Quantum-Function Testing
- Math-5285 Average-Case Metacomplexity Characterizations of One-Way Functions
- Math-5286 Size-Efficient Circuits Resilient to Short-Circuit Errors
- Math-5287 Rank Dependence of Sample Complexity in Matrix Sensing
- Math-5288 Computable Neural-Network Approximation from Noisy Samples
- Math-5289 Computable Ground Truths for Learning Problems
- Math-5290 Stochasticity and Sample Complexity in Neural Networks
- Math-5291 Open Problems in Local Graph Complexity
- Math-5292 Constraint-Satisfaction Table Caption
- Math-5293 Reduction of Guessing Problems to Source Compression
- Math-5294 Universal Compression with Large Unknown Alphabets
- Math-5295 Mutual-Information Bounds and Dimension-Free Dual Sudakov Minoration
- Math-5296 Unspecified Conic Optimization Research Problem
- Math-5297 Unspecified Flag Algebra Extremal Problem
- Math-5298 Condition-Number-Robust Low-Rank Matrix Completion
- Math-5299 Neural Network Robustness under Adversarial and Distribution Shifts
- Math-5300 Optimal Worst-Case Estimators for Signal Reconstruction